Module Focus: Grade K – Module 6
Sequence of Sessions
Overarching Objectives of this May 2014 Network Team Institute
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Module Focus sessions for K-5 will follow the sequence of the Concept Development component of the specified modules, using this narrative as a tool
for achieving deep understanding of mathematical concepts. Relevant examples of Fluency, Application, and Student Debrief will be highlighted in
order to examine the ways in which these elements contribute to and enhance conceptual understanding.
High-Level Purpose of this Session
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Focus. Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for
teaching these modules.
Coherence: P-5. Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that
develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the
same.
Standards alignment. Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the module
addresses the major work of the grade in order to fully implement the curriculum.
Implementation. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their
students while maintaining the balance of rigor that is built into the curriculum.
Related Learning Experiences
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This session is part of a sequence of Module Focus sessions examining the Grade K curriculum, A Story of Units.
Key Points
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Ordinal numbers describe the relative position of an object or action
2D shapes serve as the faces of 3D shapes and can serve as the starting point for 3D models
Smaller shapes can be systematically combined to create larger shapes
All shapes can be decomposed into smaller geometric components
Scaffolding Focused: Amplify Language
Scaffolding Focused: Move from Concrete to Representation to Abstract
Scaffolding Focused: Give Specific Guidelines for Speaking, Reading, Writing, or Listening
Session Outcomes
What do we want participants to be able to do as a result of this
session?
How will we know that they are able to do this?
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Focus. Participants will be able to identify the major work of each grade
using the Curriculum Overview document as a resource in preparation
for teaching these modules.
Coherence: P-5. Participants will draw connections between the
progression documents and the careful sequence of mathematical
concepts that develop within each module, thereby enabling participants
to enact cross- grade coherence in their classrooms and support their
colleagues to do the same. (Specific progression document to be
determined as appropriate for each grade level and module being
presented.)
Standards alignment. Participants will be able to articulate how the
topics and lessons promote mastery of the focus standards and how the
module addresses the major work of the grade in order to fully
implement the curriculum.
Implementation. Participants will be prepared to implement the
modules and to make appropriate instructional choices to meet the needs
of their students while maintaining the balance of rigor that is built into
the curriculum.
Participants will be able to articulate and demonstrate the key
points discussed.
Session Overview
Section
Introduction
Making Shapes
Review and
Adaptation
Time
Overview
Prepared Resources
Facilitator Preparation
Grade K Module 6 PPT
Facilitator Guide
Review Grade K Module 6
Review Grade K Module 6
Overview
18 min
Introduces Grade K Module 6
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68 min
Explores modeling shapes in the
world by building shapes from
components and drawing shapes
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Grade K Module 6 PPT
Facilitator Guide
Review Grade K Module 6
17 min
Review key points of Grade K
Module 6 and suggest strategies
for adapting the module for fit
time constraints
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Grade K Module 6 PPT
Facilitator Guide
Review Grade K Module 6
Session Roadmap
Section: Introduction
Time: 18 minutes
In this section, you will be introduced to the Grade K Module 6 focus Materials used include:
session.
• Grade K Module 6 PPT
• Grade K Module 6 Facilitator Guide
• Grade K Module 6 End-of-Module Assessment
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
0 min
NOTE THAT THIS SESSION IS DESIGNED TO BE 60 MINUTES IN LENGTH.
Welcome! In this module focus session, we will examine Grade K – Module
6.
1.
Turnkey Materials Provided in Addition to PowerPoint:
• GK-M6 Module Overview
• GK-M6 End-of-Module Assessment
• GK-M6 Building Flat Shapes Handout
• GK-M6 Building Solid Shape Handout
• GK-M6 Composing and Decomposing Shapes Handout
• GK-M6 Ordinal Numbers Handout
Additional Suggested Resources:
• Operations and Algebraic Thinking Progression Document
• A Story of Units: A Curriculum Overview for Grades P-5
• How to Implement A Story of Units
1 min
2.
Our objectives for this session are to:
• Examine the further development of geometric concepts and
spatial reasoning in GK-Module 6.
• Strategize for Module 6 instruction in an implementation year.
• Review the key concepts of the Kindergarten year as assessed
in the final culminating task.
• As an overall theme of this NTI, we’ve been asked to pay
special attention to the ways in which we can provide
scaffolds to support specific student needs. Before we begin
our examination of the mathematics in this module, let’s take
a few minutes to review some of the principles we can use to
GROUP
support learning.
1 min
3.
The mathematics modules were created based on the premise that
scaffolding must be folded into the curriculum in such a way that it is part of
its very DNA. The instruction in these modules is intentionally designed to
provide multiple entry points for students at all levels.
Teachers are encouraged to pay particular attention to the manner in which
knowledge is sequenced in the curriculum and to capitalize on that
sequence when working with special student populations. Most lessons
move from simple to complex allowing teachers to locate specific steps
where students are struggling or need a challenge.
That said, there are specific resources to highlight and enhance strategies
that can provide critical access for all students.
In developing the scaffolds already contained in the curriculum, Universal
Design for Learning (UDL) has provided a structure for thinking about how
to meet the needs of diverse learners. Broadly speaking, that structure asks
teachers to consider multiple means of representation; multiple means of
action and expression; and multiple means of engagement. These
dimensions promote engagement of students and provide multiple
approaches to the same content.
Individual lessons contain marginal notes to teachers (in text boxes)
highlighting specific UDL information about scaffolds that might be
employed with particular intentionality when working with students. These
tips are strategically placed in the lesson where the teacher might use the
strategy to the best advantage.
Let’s now examine additional strategies that can be considered.
In this module study, we will focus on three key ideas for developing
scaffolds that can be adapted for your classroom to meet the needs of your
students.
Explicit focus on the language of mathematics, using the development from
concrete to representation to abstract in the building of concepts, and
communicating clear expectations in instructions are areas that can provide
multiple entry points for students and can be used to promote student
learning.
1 min
4.
Much of what we share in the mathematics classroom with students is
embedded in language that is specific. Students learn casual language before
academic language. This means they may sound comfortable and fluent, but
may need additional support in their writing and speaking in an academic
environment.
Presenters should stress that academic language is an essential component
of closing the achievement gap and providing access to grade level content
and beyond.
Students may have a preconceived or informal idea of the meaning of a
mathematical term. Be specific in the definition or meaning that will be
used.
Be cautions of words with multiple meanings that might be confusing
• a garden plot and the request to plot points on a coordinate plane
Words with multiple meaning must be anticipated and then addressed, and
teachers must also be prepared to pause and provide explanations when
students identify words the teacher has not anticipated. Whenever possible,
words with multiple means should be avoided on assessments, particularly
when the meanings may be close enough to be confusing.
Make sure that Language is internally consistent (if practice problems ask
students to solve, the assessments should use the same term). If language is
not internally consistent, then different terms are highlighted and taught.
• add, plus, sum, combine, all mean the same thing
• prism, a rectangular prism, box, package all reference the same figure
in G6M5_L11
1 min
5.
The more concrete and visual these ideas can be in foundational stages, the
better!
• Use contexts that are familiar to students in your classroom.
• Use graphic organizers or other means for students to visually
organize thinking.
Note: Teachers should be thoughtful and purposeful about which graphic
organizers they select. Are teachers introducing a new concept with a need to
organize notes or are they connecting ideas comparing and contrasting? The
goal is always to help students make those connections and not use a graphic
organizer just for the novelty of it.
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1 min
6.
Consider using non-verbal displays of mathematical relationships in
your scaffolding.
Use multiple representations and multiple approaches in explaining
problems and allowing students to express solutions.
Use pictures/ visuals/ illustrations are used to make content clearer.
Each day needs structured opportunities for students to speak and write in
English.
• Students can chorally repeat key vocabulary or phrases
• Have them “turn to a neighbor and explain”
Clearly set expectations by the explicit instructions in student-friendly
language.
Use visuals in your instructions.
Be direct about language.
• Pause to discuss a vocabulary term and discuss how it may be used in
the lesson. Have students repeat the word chorally so that they can
all hear and practice.
Provide sentence frames for anyone who may benefit.
• “The volume of my prism is ___units cubed. I found this by ______.
• “My idea is similar to _____’s because ____.”
Generic/ universal sentence frames may remain posted in the classroom
throughout the year. These might include:
• “I agree with ____ because ___” or “I think the answer is _____
because...”
2 min
7.
Let’s review some key points of scaffolding instruction.
As we study the module for this session, be thinking about specific scaffolds
that might be most helpful for your classroom. We will pause at various
points in the session to intentionally examine and discuss suggestions for
scaffolds.
8.
Note to presenter:
Insert this slide at appropriate points in the module study for an in-depth look
at scaffolds. You may highlight a scaffold that already exists and discuss it or
locate a point where a student might encounter difficulty and explore options.
Delete the slide from this current sequence after you’ve inserted it in
appropriate places throughout your session.
Note to presenter: When you have inserted the slide, list several suggestions
for scaffolds that would address the situation.
Possible scaffolds:
9.
Note to presenter:
If applicable, insert this slide at an appropriate point in the module study for
an in-depth examination of a problem or task for multiple entry points
through the principles of the Universal Design for Learning (UDL).
Delete this slide from this current sequence after you’ve used it elsewhere as
needed.
REPRESENTATION: The “what” of learning.
How does the task present information and content in different ways?
How students gather facts and categorize what they see, hear, and read.
How are they identifying letters, words, or an author's style?
In this task, teachers can ...
Pre-teach vocabulary and symbols, especially in ways that build a
connection to the learners’ experience and prior knowledge by providing
text based examples and illustrations of fields. Integrate numbers and
symbols into word problems.
ACTION/EXPRESSION: The “how” of learning.
How does the task differentiate the ways that students can express what
they know?
How do they plan and perform tasks?
How do students organize and express their ideas?
In this task, teachers can...
Anchor instruction by pre-teaching critical prerequisite concepts through
demonstration or models (i.e. use of two dimensional representations of
space and geometric models).
ENGAGEMENT: The “why” of learning.
How does the task stimulate interest and motivation for learning?
How do students get engaged?
How are they challenged, excited, or interested?
In this task, teachers can...
Optimize relevance, value and authenticity by designing activities so that
learning outcomes are authentic, communicate to real audiences, and reflect
a purpose that is clear to the participants.
If available, reviewing student work would provide participants with the
opportunity to deeply understand the benefits of students sharing their
thinking in working the problem. Assessments in the module have rubrics
that clearly outline expectations and could be used in the discussion.
1 min
10.
We will begin by exploring the Module Overview to understand the purpose
of this module. We will then touch briefly on each of the eight lessons to
examine the development of the geometric concepts and use of ordinal
numbers. Our emphasis today will be on finding ways to incorporate these
objectives during an implementation year when many classes will not have
10 days of instruction to devote to Module 6.
(Note: If space permits, set up five stations with materials and instructions for
the Culminating Activity. Participants can explore these stations
independently during breaks.) Finally, we will discuss the Culminating Task
in Lesson 8 to see how it serves as a review of some of the most important
concepts of the year.
Let’s get started with the module overview.
1 min
11.
The sixth module in Grade K is Analyzing, Comparing and Composing Shapes.
The module includes 8 lessons and is allotted 10 instructional days,
including 2 days for assessment.
This module builds on understandings established in Module 2, 2D and 3 D
Shapes, and prepares students for more formal definitions of shapes and
increasingly complex composition and decomposition of shapes in Grade 1.
In particular, the decomposition of shapes will lead to the study of fractions
in Grade 1.
5 min
12.
To become familiar with Module 6, first read the narrative in the Module
Overview (pp. ii-iii).
Next, review the assessment tasks for Topics A and B. Because we may need
to modify the lessons to fit into this first year of implementation, it is
especially important for us to know how students will demonstrate mastery
of key skills.
(Provide 4-5 minutes for reading, then move to the next slide.)
3 min
13.
(Discuss the following question as a group.) What skills will the students will
need to demonstrate in the assessment?
• Use ordinal numbers to describe the relative position of an object or
action
• Identify the 2D shapes that serve as the faces of 3D shapes
• Combine smaller shapes to create larger shapes (composition)
• Decompose shapes into smaller geometric components
In order to adapt Module 6 lessons for use in a short time frame or
alternative setting, it is critical that to remember the key skills that we are
targeting. This will focus our attention and guide decision-making as we
adapt the lessons.
The Geometry Progressions document together with the progressions
document for Counting and Cardinality provide keen insight into the
relationship between the lessons and the CCLS. We will not read those
documents again in this session. However, we will connect portions of these
documents to our learning through the session.
1 min
14.
We will now give a brief overview of the objectives and activities in each
lesson in order to trace the development of the concepts through the
module. Then we will work on adapting the lessons.
Section: Making Shapes
Time: 68 minutes
In this section, you will focus on modeling shapes in the world by
building shapes from components and drawing shapes.
Materials used include:
• Grade K Module 6 PPT
• Grade K Module 6 Facilitator Guide
• Grade K Module 6 Building Flat Shapes Handout
• Grade K Module 6 Building Solid Shapes Handout
• Grade K Module 6 Composing and Decomposing Shapes
Handout
• Grade K Module 6 Ordinal Numbers Handout
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
5 min
Lesson Objective: Describe the systematic construction of flat shapes using
ordinal numbers.
15.
This lesson addresses the standard in K.G.5: “Model shapes in the world by
building shapes from components (e.g. sticks and clay balls) and drawing
shapes.”
Note to presenter: If time permits, facilitate the construction of a square with
the participants, using ½ of a stir stick for each side and connecting the
corners with a small piece of the clay, mirroring the activity in the concept
development. Then encourage them to create other equilateral shapes.
GROUP
5 min
16.
Lesson Objective: Build flat shapes with varying side lengths and record
with drawings.
This is a continuation of K.G.5 and also dovetails with MP4 (model with
mathematics) and MP6 (attend to precision).
Note to presenter: If time permits, using the stir sticks and clay, encourage the
participants to create various shapes with sides of different lengths. Ask them
to recreate these shapes on their whiteboards and share with their table
mates.
5 min
17.
Lesson Objective: Compose solids using flat shapes as a foundation.
Geometric Progressions document page 6: “Students also begin to name and
describe three-dimensional shapes with mathematical vocabulary, such as
“sphere”, “cube”, “cylinder”, and “cone”. They identify faces of threedimensional shapes as two-dimensional geometric figures and explicitly
identify shapes as two-dimensional (“flat” or lying in a plane) or threedimensional (”solid”).
In this lesson, children have the opportunity to build on their understanding
of faces by using their square constructions as a basis for creating cubes.
Note to presenter: If time permits, extend the activity. First, review the names
and the attributes of the solids with the participants. In particular, examine
the attributes of the cube carefully. Then, facilitate the construction of the
skeleton of a cube, using the square created before and other ½ lengths of stir
sticks. This mirrors the activity in the concept development for Lesson 3.
8 min
18.
Why are ordinal numbers in this module?
Progressions Document Page 6:
“Understanding and describing shapes and space is one of the two critical
areas of Kindergarten mathematics. Students develop geometric concepts
and spatial reasoning from experience with two perspectives on space: the
shapes of objects and the relative positions of objects.”
K.CC.4d: Describe a set of objects using ordinal terms. MP.6
3 min
19.
Geometric Progressions document page 7:
A second important area for kindergartners is the composition of geometric
figures. Students not only build shapes from components, but also compose
shapes to build pictures and designs. Initially lacking competence in
composing geometric shapes, they gain ability to combine shapes--first by
trial and error and gradually by considering components--into pictures.
The pictures that children initially create may be of real world objects, like
the house, but they also begin to make more irregular shapes. Think back to
when you had to calculate the area of an irregular shape. How does this
work in Kindergarten prepare children to calculate area of irregular shapes
later? (Children can break down the irregular shape into a regular shape for
which they have an area equation.)
3 min
20.
In the last lesson, students utilized smaller shapes to construct larger
composite shapes. In this lesson, they will reverse the process and learn to
decompose shapes into smaller parts. This anticipates shape decomposition
into equal parts, leading to the study of fractions in Grade 1.
Look at the parallelogram on the bottom right. How could that that outline
be filled to show fourths?
6 min
21.
Progressions Document page 7:
Students combine two-dimensional shapes and solve problems such as
deciding which piece will fit into a space in a puzzle, intuitively using
geometric motions (slides, flips, and turns, the informal names for
translations, reflections, and rotations, respectively). They can construct
their own outline puzzles and exchange them, solving each other’s.
Note to presenter: If time permits, ask the participants to cut out the squares
from the shape template from Lesson 7. As in the concept development for this
lesson, ask them to draw two lines edge-to-edge across the shape and then to
cut on the lines to decompose the shape. Then, they exchange their pieces with
a partner and reconstruct the square. Time permitting, they may repeat the
activity with the rectangle.
3 min
22.
Allow two minutes for discussion. Allow participants to share their
observations.
How does the progression of Lessons 5-7 mirror the progression of
number decomposition in earlier modules of A Story of Units?
They start with composition and look at decomposition as finding
something smaller hiding inside (think back to Module 1-Lesson 9 and
finding hidden numbers in the 5-sticks).
How does the decomposition of shapes prepares students for
understanding fractions in Grade 1?
Fractions involve decomposing shapes into equal portions, which is
decomposition.
30 min
23.
The final lesson in Module 6 is a culminating task that allows students to
demonstrate their understanding of skills learned throughout the year. They
will have an opportunity to compose and decompose both numbers and
shape, use math models, write word problems, and use their measurement
skills.
Section: Review and Adaptation
Time: 17 minutes
In this section, you will focus on strategies for adapting concepts
and lessons to fit while facing time and calendar constraints while
reviewing key concepts of Grade K Module 6.
Materials used include:
• Grade K Module 6 PPT
• Grade K Module 6 Facilitator Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
1 min
During the first year of implementation, time is especially tight. Many
teachers and schools already know that they will not have 10 full days for
implementing Module 6. In order for students to leave Kindergarten having
fully covered the math standards, teachers will have to be creative with time
and implementation.
24.
Let’s get creative!
GROUP
25.
If you are searching for time to fit in aspects of Module 6, consider the
following:
• Any remaining days after Module 5 is complete
• During 1:1 assessment
• Module 5 Fluency
• Morning Meeting
• Testing days when specials are cancelled
26.
Provide an example for each of the ideas listed.
• Adapt Concept Development into a mini-lesson and provide
independent work time during centers or 1:1 assessments. Take
Lesson 5 as an example. Spend 5 minutes demonstrating how to put
pattern blocks together to form other shapes and trace. Send
children to work with a partner to do the same using the Problem
Set. Use pattern block templates to extend their independent
practice. If possible, bring group together for a mini-debrief and ask 1
key question.
• Incorporate M6 Fluency activities or look for ways to modify
concept for Fluency instruction. In Module 5, provide students
with a set of 11-19 pattern blocks. Have children count out 10 blocks
and some more blocks. Have them create a new shape with the 10
blocks and a separate shape with the extras.
• Look for other natural ways to weave concepts into the day.
Work with ordinal numbers when standing in line. It’s also easy to
incorporate first-third into directions.
• Select key lessons for remaining instructional days. If a concept
doesn’t lend itself to any of the other options, save it for the
remaining instructional days and use the original lesson plan.
10 min
1 min
27.
Create groups of 4-8 participants. Assign each group one of the four key skills
and distribute the appropriate packet.
• Ordinal Numbers
• Building Flat Shapes
• Building Solid Shapes
• Composing and Decomposing Shapes
Provide 10 minutes of work time for participants to review the relevant
material and propose an adaptation that could work for them in this first year
of implementation.
28.
Give each group a chance to quickly present their ideas. If time permits, they
can model the adaptation. Provoke conversation with the following questions:
• Does this get at the heart of the target skill?
• Will students be able to demonstrate mastery of the skill on the
assessment after this lesson?
29.
Let’s wrap up the session by reviewing the key points of Module 6.
2 min
30.
Let’s review some key points of this session.
• Ordinal numbers describe the relative position of an object or timing
of an action
• 2D shapes serve as the faces of 3D shapes and can serve as the
starting point for 3D models
• Smaller shapes can be systematically combined to create larger
shapes
• All shapes can be decomposed into smaller geometric components
3 min
31.
Take two minutes to turn and talk with others at your table. During this
session, what information was particularly helpful and/or insightful? What
new questions do you have?
Use the following icons in the script to indicate different learning modes.
Video
Turnkey Materials Provided
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Grade K Module 6 PPT
Grade K Module 6 Facilitator Guide
Grade K Module 6 Module Overview
Reflect on a prompt
Active learning
Turn and talk
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Grade K Module 6 End-of-Module Assessment
Grade K Module 6 Building Flat Shapes Handout
Grade K Module 6 Building Solid Shapes Handout
Grade K Module 6 Composing and Decomposing Shapes Handout
Grade K Module 6 Ordinal Numbers Handout
Additional Suggested Resources
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How to Implement A Story of Units
A Story of Units Year Long Curriculum Overview
A Story of Units CCLS Checklist
Operations and Algebraic Thinking Progression Document